My oldest turn 12 last year and he took his safety course. One question I had was, do you need to take a different safety course for each state? The outcome of this was no. We're Indiana residents, he took a Michigan course and he was good for Indiana, Wisconsin, and Michigan. I don't know about any other states, but it sounds as if you have the certification from at least one state you're good.
We were pulled over in Wisconsin to check trail passes. and no they were not on our sleds only because we bought them online and they hadn't shipped yet. The cops were great, and we're happy to see he had everything in order. That was only his second trip riding on his own and he did very good!